Final answer:
The 25th term of the arithmetic progression is found using the formula Tn = a + (n - 1)d. With a first term of -5 and a common difference of 5, the 25th term is 115, which does not match any of the provided options.
Step-by-step explanation:
The question is asking to find the 25th term of the arithmetic progression (AP) with the first few terms being -5, -5/2, 0, 5/2,.... To find any term in an arithmetic progression, we can use the formula:
Tn = a + (n - 1)d
where Tn is the n-th term, a is the first term, d is the common difference, and n is the term number.
In this sequence, the first term a = -5 and the difference between the terms d = 5/2 - (-5) which is 5/2 + 5/2 or 5. Now we can use these values to find the 25th term with the formula:
T25 = -5 + (25 - 1) × 5
Calculating the above expression, we get:
T25 = -5 + (24 × 5)
T25 = -5 + 120
T25 = 115
Thus, the 25th term of the given arithmetic progression is 115, which is not listed in the provided options.